Ground-state properties of even-evenN=Znuclei within the Hartree-Fock-BCS and higher Tamm–Dancoff approaches

Abstract

We calculate the ground-state properties of well deformed, even-even $N=Z$ nuclei in the region between $^{56}\mathrm{Ni}$ and $^{100}\mathrm{Sn}$ within two different approaches, focusing on the binding energy and deformation and pairing properties. First, we employ the Hartree-Fock-BCS (HFBCS) approximation with the Skyrme effective nucleon-nucleon interaction and discuss how the results depend on the parametrization of the interaction and on the pairing force parameters adjusted in various schemes to reproduce the experimental odd-even mass differences. Then, within the Higher Tamm-Dancoff Approximation (HTDA), which explicitly conserves the particle number, we calculate the same properties starting from the HFBCS solutions. The HTDA treatment of the ground-state correlations is converged within a $n$-particle-$n$-hole expansion using up to $n=4$ particle-hole excitations of the pair type (in the sense of Cooper pairs). We compare the ground-state properties calculated in these two descriptions of pairing correlations and deduce the importance of the particle-number conservation in weak pairing regimes. Finally, we extend the HTDA calculations so as to include the proton-neutron residual interaction and investigate the role of proton-neutron pairing on the above ground-state properties.